Two new polls show incumbent Democratic Sen. Kay Hagan of North Carolina with an edge over Republican challenger Thom Tillis in a race that will play a crucial role in determining which party controls the U.S. Senate after November.

Among likely voters, Ms. Hagan holds a 4-point edge at about 45 percent to 41 percent over Mr. Tillis in an Elon University survey conducted from Sept. 5-9 and has a slightly larger lead, about 43 percent to 37 percent, among registered voters.

Libertarian party candidate Sean Haugh was not included in the survey, but 9 percent of likely voters and about 11 percent of registered voters chose “someone else.”

Democrats hold an effective 55-45 advantage in the Senate, but races for open seats controlled by Democrats in South Dakota, Montana and West Virginia are likely to go to the GOP.

That means Republicans need to pick up a net of three seats out of about a half dozen competitive races against Democratic incumbents, including in red states like Alaska, Arkansas, Louisiana and North Carolina, in order to re-take a majority in the upper chamber.

The GOP is also defending seats in several competitive races in Kentucky, Georgia and Kansas.